New budget estimates Tuesday reflect an improved economy and slower growth in per capita health care costs but still stubbornly high deficits adding roughly between $6 trillion to $9 trillion in debt over the next 10 years.

The government is predicted to end this fiscal year $845 billion in the red. Deficits will fall for the next few years but then rise again to $978 billion by 2023 — even if threatened across-the-board cuts go into effect March 1.

The numbers underscore the persistent tension between reducing the deficit and helping along the economic recovery. Indeed, if the cuts were to go into effect on top of tax increases already enacted, it will cost the economy about one percent of GDP in 2013.

The 74-page report, prepared by the Congressional Budget Office, is the most complete assessment yet of the government’s fiscal outlook since the New Year’s Day tax deal reached between the White House and Republicans.

That agreement allowed rates to rise for upper-income households but just as important it made permanent Bush-era tax breaks that will cost trillions of dollars, thereby widening the deficit by CBO’s count.

The bright spots for CBO include a clear improvement — from past estimates — in the rate of growth in health care costs. And as the economy improves, there will be a period in which deficits will fall as low as $430 billion in 2015.

But as more baby boomers retire, the upward pressure on the deficit resumes, getting back to the $1 trillion range that has been the bitter experience of recent years.

House Republicans are sure to seize on CBO’s analysis as further evidence that more savings must be found through fundamental changes in Medicare. But the report also shows the staggering challenge the GOP faces if it really intends to wipe out all deficit by 2023.

This has been a goal recently promoted by House Budget Committee Chairman Paul Ryan (R-Wis.), yet the closest such scenario in the CBO report is one demanding $4 trillion in deficit reduction over the next 10 years — on top of the March cuts. Since Republicans have opposed new taxes, that would mean a dramatic impact on government programs. And in the short term at least CBO predicts that economic growth will be slower and real GDP .6 percent less in the fourth quarter of 2014.

Tuesday’s release comes at a critical juncture for both Congress and President Barack Obama addressed the budget picture only minutes later at the White House.

“We can’t just cut our way to prosperity” Obama told reporters, and the president argued for some delay in the March cuts until a longer term solution can be found this spring or summer.

These automatic spending cuts March 1 will fall most heavily on annual appropriations for defense and domestic programs, and the military services are already struggling under caps set in a six-month continuing resolution that has governed spending since Oct. 1.

That resolution expires March 27 and even before any sequester, military chiefs are warning that serious cuts will have to be made in operating accounts unless there is some relief allowed for the remainder of this fiscal year.

New charts from the Army this week paint a dire picture, showing a $6 billion shortfall under the CR, aggravated further by increased supply and transportation costs related to the U.S. military and civilian presence in Afghanistan. Even the Marines have weighed in: a letter from Gen. James Amos, the commandant, warned the Senate Armed Services Committee of a $406 million shortfall in 2013 without some adjustment in the CR.

In the midst of all this turmoil, the White House is expected to finally deliver its own 2014 budget plan sometime in March. And the administration insists that Obama’s last offer remains on the table to substitute a combination of roughly $900 billion in savings and $600 billion in revenues.

This would include about $600 billion from health care programs like Medicare and Medicaid as well as other benefit programs, such as food stamps and farm subsidies. An estimated $200 billion, divided between defense and domestic programs, would still come from appropriations. And the remainder — in the range of $100 billion — is attributed to proposed changes in the CPI index used to calculate annual inflation adjustments to federal programs.

Hoping still to salvage some progress on corporate tax reform, the administration is relying heavily on personal income taxes to meet its new revenue demands. Of the estimated $600 billion sought by Obama, for example, more than 80 percent would come from his plan to cap deductions for the wealthy at a 28 percent rate.

Republicans have flatly ruled out this approach — having given ground already on income taxes. But even as the CBO was releasing its report Tuesday afternoon, the day’s events underscored how the GOP is torn itself at what direction to take.

Debate on the House floor focused on legislation demanding that Obama submit a balanced budget plan by April 1 — a huge task given the CBO numbers. At the same time, Majority Leader Eric Cantor (R-Va.) seemed most intent on changing the subject in what was billed a major policy speech titled Making Life Work.